In neuro-fuzzy systems, the input/output behavior of fuzzy systems can be optimized by using neural networks. This allows the disadvantages of fuzzy systems and of neural networks to be compensated for.
One possible method of optimizing a fuzzy system by means of a neural network is to transform a fuzzy system into a neural network and to train the latter using input/output measured values. While in the fuzzy system the system behavior of a technical process to be simulated can be introduced, the transformation into a neural network permits additional optimization with the aid of input/output measured values of the technical process to be simulated. The optimization can in this case be automated by optimization algorithms, which can be executed by the neuro-fuzzy system with the aid of a computer.
Various methods for transforming the components of a fuzzy system into the structures of a neural network are known. In particular, a fuzzy system has a fuzzy logic system which, as a rule, comprises the three components xe2x80x9cfuzzificationxe2x80x9d, xe2x80x9ccontrol arrayxe2x80x9d and xe2x80x9cdefuzzificationxe2x80x9d. The three components can be depicted in each case by using specific types of neuron. The basic structure of a neuro-fuzzy system, that is to say the individual components of the fuzzy logic system within a neuro-fuzzy network, are illustrated in FIG. 1. During the transformation of the fuzzy logic system FS into the neural network NN, the components fuzzification F, rule base R and defuzzification D are simulated in the neural network NN as a neural fuzzification network NF, a neural rule base network NR and a neural defuzzification network ND.
As a rule, trapezoidal or triangular membership functions are used for the purpose of fuzzification. Their depiction in the neural network is generally carried out using sigmoid or Gaussian functions.
FIG. 2 illustrates, by way of example, a trapezoidal membership function Z having the parameters X0, X1, X2 and X3. This membership function Z has a nonlinear profile and is normalized to a normalized value range [0,1] of the fuzzy logic system FS, said range as a rule having a maximum value MW of magnitude 1.
FIG. 3 shows, by way of example, a transformation, bearing the reference symbol NZ of the membership function Z illustrated in FIG. 2 in the neural network NN. The simulation of nonlinear transfer functions in the fuzzy logic system FS, such as the trapezoidal membership function Z, for example, is preferably carried out in the neural network NN by means of sigmoid functions.
German Patent DE 195 28 984 describes a method of transforming a fuzzy logic system into a neural network, sigmoid functions being linked together multiplicatively in order to simulate membership functions. Multiplicative linking of sigmoid functions in this way is illustrated in FIG. 4. In this case, the sigmoid functions f and g have the parameters xcexc1, 1 and xcexc2, 2.
FIG. 5 illustrates, by way of example, a result function y1 of the simulation in the neural network NN of a nonlinear, trapezoidal membership function Z of the fuzzy logic system FS. The transformation into the neural network NN is associated with the action of presetting the parameters xcexc1, 1, xcexc2, 2 of the sigmoid functions f and g. As a result of optimizing the neural network NN, in particular using input/output measured values, the parameters xcexc1, 1, xcexc2, 2 of the sigmoid functions f and g, and hence their profile, are changed.
In the abovementioned method, the case may occur in which the parameters xcexc1, 1, xcexc2, 2 change in such a way that back-transformation of the neural network NN into a fuzzy logic system FS is not readily possible. This is illustrated by way of example in FIG. 6, in which the profile of a result function y1xe2x80x2 reached by means of optimizing the neural network NN is illustrated.
Since the value range of the membership function y1xe2x80x2 no longer corresponds to that of the sigmoid functions f and g, back-transformation into the fuzzy logic system FS is no longer possible. The consequence of this is that a neuro-fuzzy system of this type is constructed as a neural network following optimization and has neural structures, but can no longer be operated as a pure fuzzy system. As a result, practical implementation, for example by means of standardized, commercially available fuzzy system software, is no longer possible.
The reference Proceedings of the IEEE, Vol. 83, No. 3, March 1995, pages 378 to 406, xe2x80x9cNeuro-Fuzzy Modeling and Controlxe2x80x9d describes, in order to simulate membership functions from two sigmoid functions, taking the product or the absolute magnitude of their difference. Even in the case of simulation by forming the difference and magnitude, it is possible for the case described above to occur in which, following the training of the neural network, the value range of the membership function no longer corresponds to that of the sigmoid functions. Back-transformation of the trained neural network into a pure fuzzy system is then no longer possible. In addition, the formation of the magnitude is no longer possible with standard neurons, such as summing or product neurons. Since magnitude neurons cannot readily be differentiated, the training of the neuron network requires additional case decisions, as a result of which practical implementation, for example by means of standardized, commercially available fuzzy system software, is no longer possible.
An object of the present invention is to specify a method of transforming a fuzzy logic system into a neural network where, in order to simulate membership functions, sigmoid functions are linked together in such a way that, even after the optimization of the neural network, back-transformation of the neural network into a fuzzy logic system is possible.
An advantage of the method according to the present invention is that a fuzzy logic system can be transformed, in particular component by component, into a neural network and the latter can then be optimized as a whole, i.e. all the components together.
Thus, in addition to the system behavior which can be taken into account in the fuzzy logic system, such as, for example, the number of membership functions to be used, measurement data from the technical process to be simulated can be introduced into the optimization method of the neural network. The method according to the present invention for transforming the triangular or trapezoidal membership functions in particular permits their parameters in the neural network to be varied during the optimization of the latter only in such a way that in every case subsequent back-transformation of the neural network into an optimized fuzzy logic system can take place.
An advantage of a neuro-fuzzy system according to the present invention for transforming the fuzzy logic system into a neural network is thus ultimately to obtain an appropriately optimized fuzzy logic system, as a result of the possibility of back-transforming the trained neural network. This advantageously makes it possible to use, in particular, standardized fuzzy system software for describing the optimized fuzzy logic system.